Deep Thinking What Mathematics Can Teach Us About The Mind
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Deep Thinking What Mathematics Can Teach Us About The Mind
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Author : William Byers
language : en
Publisher: World Scientific
Release Date : 2014-09-22
Deep Thinking What Mathematics Can Teach Us About The Mind written by William Byers and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-22 with Mathematics categories.
There is more than one way to think. Most people are familiar with the systematic, rule-based thinking that one finds in a mathematical proof or a computer program. But such thinking does not produce breakthroughs in mathematics and science nor is it the kind of thinking that results in significant learning. Deep thinking is a different and more basic way of using the mind. It results in the discontinuous “aha!” experience, which is the essence of creativity. It is at the heart of every paradigm shift or reframing of a problematic situation.The identification of deep thinking as the default state of the mind has the potential to reframe our current approach to technological change, education, and the nature of mathematics and science. For example, there is an unbridgeable gap between deep thinking and computer simulations of thinking. Many people suspect that such a gap exists, but find it difficult to make this intuition precise. This book identifies the way in which the authentic intelligence of deep thinking differs from the artificial intelligence of “big data” and “analytics”.Deep thinking is the essential ingredient in every significant learning experience, which leads to a new way to think about education. It is also essential to the construction of conceptual systems that are at the heart of mathematics and science, and of the technologies that shape the modern world. Deep thinking can be found whenever one conceptual system morphs into another.The sources of this study include the cognitive development of numbers in children, neuropsychology, the study of creativity, and the historical development of mathematics and science. The approach is unusual and original. It comes out of the author's lengthy experience as a mathematician, teacher, and writer of books about mathematics and science, such as How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics and The Blind Spot: Science and the Crisis of Uncertainty.
Deep Thinking
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Author : William Byers
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2015
Deep Thinking written by William Byers and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Education categories.
There is more than one way to think. Most people are familiar with the systematic, rule-based thinking that one finds in a mathematical proof or a computer program. But such thinking does not produce breakthroughs in mathematics and science nor is it the kind of thinking that results in significant learning. Deep thinking is a different and more basic way of using the mind. It results in the discontinuous "aha!" experience, which is the essence of creativity. It is at the heart of every paradigm shift or reframing of a problematic situation. The identification of deep thinking as the default state of the mind has the potential to reframe our current approach to technological change, education, and the nature of mathematics and science. For example, there is an unbridgeable gap between deep thinking and computer simulations of thinking. Many people suspect that such a gap exists, but find it difficult to make this intuition precise. This book identifies the way in which the authentic intelligence of deep thinking differs from the artificial intelligence of "big data" and "analytics." Deep thinking is the essential ingredient in every significant learning experience, which leads to a new way to think about education. It is also essential to the construction of conceptual systems that are at the heart of mathematics and science, and of the technologies that shape the modern world. Deep thinking can be found whenever one conceptual system morphs into another. The sources of this study include the cognitive development of numbers in children, neuropsychology, the study of creativity, and the historical development of mathematics and science. The approach is unusual and original. It comes out of the author's lengthy experience as a mathematician, teacher, and writer of books about mathematics and science, such as How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics and The Blind Spot: Science and the Crisis of Uncertainty.
Ancient Greek I
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Author : Philip S. Peek
language : en
Publisher: Open Book Publishers
Release Date : 2021-10-19
Ancient Greek I written by Philip S. Peek and has been published by Open Book Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-19 with Literary Collections categories.
In this elementary textbook, Philip S. Peek draws on his twenty-five years of teaching experience to present the ancient Greek language in an imaginative and accessible way that promotes creativity, deep learning, and diversity. The course is built on three pillars: memory, analysis, and logic. Readers memorize the top 250 most frequently occurring ancient Greek words, the essential word endings, the eight parts of speech, and the grammatical concepts they will most frequently encounter when reading authentic ancient texts. Analysis and logic exercises enable the translation and parsing of genuine ancient Greek sentences, with compelling reading selections in English and in Greek offering starting points for contemplation, debate, and reflection. A series of embedded Learning Tips help teachers and students to think in practical and imaginative ways about how they learn. This combination of memory-based learning and concept- and skill-based learning gradually builds the confidence of the reader, teaching them how to learn by guiding them from a familiarity with the basics to proficiency in reading this beautiful language. Ancient Greek I: A 21st-Century Approach is written for high-school and university students, but is an instructive and rewarding text for anyone who wishes to learn ancient Greek.
Handbook Of The History And Philosophy Of Mathematical Practice
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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date :
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Thinking As Researchers Innovative Research Methodology Content And Methods
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Author : Nagwa Babiker Abdulla Yousif
language : en
Publisher: Xlibris Corporation
Release Date : 2023-02-12
Thinking As Researchers Innovative Research Methodology Content And Methods written by Nagwa Babiker Abdulla Yousif and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-12 with Reference categories.
This book is appropriate for undergraduate and graduate research methods courses as well as for instructors, academicians, social researchers, social workers and community development planners. The book aims to give a brief summary about the critical thinking and innovative research methods which are crucial in academic's promotion and knowledge building. Social Research Methods is one of the most important courses in the educational curriculum that adequately support students and researchers acquire the competencies they need to deal with complex data and new analytical tools. World is changing and accordingly, there are changing in the nature of data (for instance, big data, analytics etc.), and the complexity of the environment. University' instructors have to incorporate research in the undergraduate curriculum to allow the students to gain the knowledge and skills to learn the research process, not to conduct it per se, but, rather to use the research to bridge the gap between knowledge and critical decision-making.
The Best Writing On Mathematics 2015
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Author : Mircea Pitici
language : en
Publisher: Princeton University Press
Release Date : 2016-01-12
The Best Writing On Mathematics 2015 written by Mircea Pitici and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-12 with Mathematics categories.
The year's finest writing on mathematics from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2015 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here David Hand explains why we should actually expect unlikely coincidences to happen; Arthur Benjamin and Ethan Brown unveil techniques for improvising custom-made magic number squares; Dana Mackenzie describes how mathematicians are making essential contributions to the development of synthetic biology; Steven Strogatz tells us why it’s worth writing about math for people who are alienated from it; Lisa Rougetet traces the earliest written descriptions of Nim, a popular game of mathematical strategy; Scott Aaronson looks at the unexpected implications of testing numbers for randomness; and much, much more. In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.
Humanizing Mathematics And Its Philosophy
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Author : Bharath Sriraman
language : en
Publisher: Birkhäuser
Release Date : 2017-11-07
Humanizing Mathematics And Its Philosophy written by Bharath Sriraman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with Mathematics categories.
This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.
How Not To Be Wrong
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Author : Jordan Ellenberg
language : en
Publisher: National Geographic Books
Release Date : 2015-05-26
How Not To Be Wrong written by Jordan Ellenberg and has been published by National Geographic Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-26 with Mathematics categories.
“Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
How Mathematicians Think
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Author : William Byers
language : en
Publisher: Princeton University Press
Release Date : 2010-05-02
How Mathematicians Think written by William Byers and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-02 with Mathematics categories.
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
The Psychology Of Wisdom
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Author : Robert J. Sternberg
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
The Psychology Of Wisdom written by Robert J. Sternberg and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Psychology categories.
The Psychology of Wisdom: An Introduction is the first comprehensive coursebook on wisdom, providing an engaging, balanced, and expert introduction to the psychology of wisdom. It provides a comprehensive and up-to-date account of the psychological science of wisdom, covering wide-ranging perspectives. Each chapter includes extensive pedagogy, including a summary, a glossary, bolded terms, practical applications, discussion questions, and a brief description of the authors' research. Topics include the philosophical foundations, folk conceptions, and psychological theories of wisdom; relations of wisdom to morality and ethics, to personality and well-being, to emotion; wisdom and leadership, wisdom and social policy. These topics are covered in a non-technical, bias-free, and student-friendly manner. Written by the most eminent experts in the field, this is the definitive coursebook for undergraduate and graduate students, as well as interested professionals and researchers.